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mfair: Matrix Factorization with Auxiliary Information in R
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The R packagemfair implements the methods based on the paperMFAI:A scalable Bayesian matrix factorization approach to leveragingauxiliary information. MFAIintegrates gradient boosted trees in the probabilistic matrixfactorization framework to leverage auxiliary information effectivelyand adaptively.
Note: Two years later, I realized there are a bunch of areas forimprovement in my code. Taking memory management as an example, usingfunctions likec(),append(),cbind(), orrbind() to dynamicallygrow variables is not recommended, especially with large datasets. Amore efficient approach is to pre-allocate memory if the output size isknown. If you don’t know the size, a good way is to store outputs in alist. You can merge them afterwards using functions likelapply() anddo.call(). For more details, please refer toAdvanced R Chapter 24Improving performance orAdvanced R Course Chapter 5Performance.
For a quick start, you can install the development version ofmfairfromGitHub with:
# install.packages("devtools")devtools::install_github("YangLabHKUST/mfair")
For more illustration and examples, you can alternatively use:
# install.packages("devtools")devtools::install_github("YangLabHKUST/mfair",build_vignettes=TRUE)
to build vignettes simultaneously. Please note that it can take a fewmore minutes.
- This is a basic example which shows you how to solve a common problem:
set.seed(20230306)library(mfair)# Simulate data# Set the data dimension and rankN<-100M<-200K_true<-2L# Set the proportion of variance explained (PVE)PVE_Z<-0.9PVE_Y<-0.5# Generate auxiliary information XX1<- runif(N,min=-10,max=10)X2<- runif(N,min=-10,max=10)X<- cbind(X1,X2)# F(X)FX1<-X1/2-X2FX2<- (X1^2-X2^2+2*X1*X2)/10FX<- cbind(FX1,FX2)# Generate the factor matrix Z (= F(X) + noise)sig1_sq<- var(FX1)* (1/PVE_Z-1)Z1<-FX1+ rnorm(n=N,mean=0,sd= sqrt(sig1_sq))sig2_sq<- var(FX2)* (1/PVE_Z-1)Z2<-FX2+ rnorm(n=N,mean=0,sd= sqrt(sig2_sq))Z<- cbind(Z1,Z2)# Generate the loading matrix WW<-matrix(rnorm(M*K_true),nrow=M,ncol=K_true)# Generate the main data matrix Y_obs (= Y + noise)Y<-Z%*% t(W)Y_var<- var(as.vector(Y))epsilon_sq<-Y_var* (1/PVE_Y-1)Y_obs<-Y+matrix( rnorm(N*M,mean=0,sd= sqrt(epsilon_sq) ),nrow=N,ncol=M)# Create MFAIR objectmfairObject<- createMFAIR(Y_obs, as.data.frame(X),K_max=K_true)#> The main data matrix Y is completely observed!#> The main data matrix Y has been centered with mean = 0.196418181646673!# Fit the MFAI modelmfairObject<- fitGreedy(mfairObject,sf_para=list(verbose_loop=FALSE))#> Set K_max = 2!#> Initialize the parameters of Factor 1......#> After 2 iterations Stage 1 ends!#> After 77 iterations Stage 2 ends!#> Factor 1 retained!#> Initialize the parameters of Factor 2......#> After 2 iterations Stage 1 ends!#> After 78 iterations Stage 2 ends!#> Factor 2 retained!# Prediction based on the low-rank approximationY_hat<- predict(mfairObject)#> The main data matrix Y has no missing entries!# Root-mean-square-errorsqrt(mean((Y_obs-Y_hat)^2))#> [1] 11.04169# Predicted/true matrix variance ratiovar(as.vector(Y_hat))/ var(as.vector(Y_obs))#> [1] 0.466571# Prediction/noise variance ratiovar(as.vector(Y_hat))/ var(as.vector(Y_obs-Y_hat))#> [1] 0.9493455
mfaircan also handle the matrix with missing entries:
# Split the data into the training set and test setn_all<-N*Mtraining_ratio<-0.5train_set<- sample(1:n_all,n_all*training_ratio,replace=FALSE)Y_train<-Y_test<-Y_obsY_train[-train_set]<-NAY_test[train_set]<-NA# Create MFAIR objectmfairObject<- createMFAIR(Y_train, as.data.frame(X),Y_sparse=TRUE,K_max=K_true)#> The main data matrix Y has 50% missing entries!#> The main data matrix Y has been transferred to the sparse mode!#> The main data matrix Y has been centered with mean = 0.0364079914822442!# Fit the MFAI modelmfairObject<- fitGreedy(mfairObject,sf_para=list(verbose_loop=FALSE))#> Set K_max = 2!#> Initialize the parameters of Factor 1......#> After 2 iterations Stage 1 ends!#> After 99 iterations Stage 2 ends!#> Factor 1 retained!#> Initialize the parameters of Factor 2......#> After 2 iterations Stage 1 ends!#> After 68 iterations Stage 2 ends!#> Factor 2 retained!# Prediction based on the low-rank approximationY_hat<- predict(mfairObject)# Root-mean-square-errorsqrt(mean((Y_test-Y_hat)^2,na.rm=TRUE))#> [1] 11.6532# Predicted/true matrix variance ratiovar(as.vector(Y_hat),na.rm=TRUE)/ var(as.vector(Y_obs),na.rm=TRUE)#> [1] 0.4505973# Prediction/noise variance ratiovar(as.vector(Y_hat),na.rm=TRUE)/ var(as.vector(Y_obs-Y_hat),na.rm=TRUE)#> [1] 0.8830444
- Empirically, the backfitting algorithm can further improve theperformance:
# Refine the MFAI model with the backfitting algorithmmfairObject<- fitBack(mfairObject,verbose_bf_inner=FALSE,sf_para=list(verbose_sf=FALSE,verbose_loop=FALSE))#> Iteration: 1, relative difference of model parameters: 0.2827721.#> Iteration: 2, relative difference of model parameters: 0.05223744.#> Iteration: 3, relative difference of model parameters: 0.07034077.#> Iteration: 4, relative difference of model parameters: 0.08374642.#> Iteration: 5, relative difference of model parameters: 0.009833483.# Prediction based on the low-rank approximationY_hat<- predict(mfairObject)# Root-mean-square-errorsqrt(mean((Y_test-Y_hat)^2,na.rm=TRUE))#> [1] 11.63093# Predicted/true matrix variance ratiovar(as.vector(Y_hat),na.rm=TRUE)/ var(as.vector(Y_obs),na.rm=TRUE)#> [1] 0.4697753# Prediction/noise variance ratiovar(as.vector(Y_hat),na.rm=TRUE)/ var(as.vector(Y_obs-Y_hat),na.rm=TRUE)#> [1] 0.9254147
vignette("ml100k")- Explore thevignette illustrating the spatial and temporal dynamicsof gene regulation among braintissues:
vignette("neocortex")- For more documentation and examples, please visit our packagewebsite.
If you find themfair package or any of the source code in thisrepository useful for your work, please cite:
Wang, Z., Zhang, F., Zheng, C., Hu, X., Cai, M., & Yang, C. (2024).MFAI: A Scalable Bayesian Matrix Factorization Approach to LeveragingAuxiliary Information.Journal of Computational and GraphicalStatistics, 33(4), 1339–1349.https://doi.org/10.1080/10618600.2024.2319160
The R packagemfair is developed and maintained byZhiweiWang.
Please feel free to contactZhiweiWang,Prof. MingxuanCai, orProf. CanYang if any inquiries.
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mfair: Matrix Factorization with Auxiliary Information in R